The fundamental challenge of data visualization lies in the translation of numerical values into spatial dimensions, a process that, if handled without mathematical rigor, can lead to significant public misinformation. Robert Kosara, a prominent figure in the data visualization community and creator of the EagerEyes platform, recently addressed this critical issue through a comprehensive motion-graphics production titled "Linear vs. Quadratic Change." The video serves as a technical deep dive into the common errors found in infographic design, particularly the unintended distortion that occurs when designers scale two-dimensional objects to represent one-dimensional data. This phenomenon, often referred to in academic circles as the "Lie Factor," remains a persistent hurdle in the quest for visual integrity within news media and corporate reporting.
The Mathematical Foundation of Visual Distortion
At the heart of Kosara’s analysis is the geometric relationship between linear dimensions and area. In many "pictorial" bar charts—infographics that use icons like people, cars, or money bags instead of simple rectangles—designers frequently scale the entire graphic to match a data point. However, if a value doubles and the designer doubles both the height and the width of the icon to maintain its aspect ratio, the resulting area of the icon does not double; it quadruples. This is known as quadratic growth ($Area = side^2$).
This mathematical reality creates a visual "lie" where the viewer perceives a much larger change than the data actually supports. For example, if an icon representing a $100 budget is scaled up to represent a $200 budget by doubling its height and width, the new icon occupies four times the physical space on the page or screen. The human eye is naturally inclined to perceive the total area or volume of an object rather than just its vertical height, leading to a profound exaggeration of the underlying statistics. Kosara notes that this issue is not limited to simple icons but extends to more complex visualizations, such as polar area diagrams or "rose diagrams," where the area of a circle wedge grows with the square of the radius. Without careful adjustment, these charts can inadvertently mislead even the most discerning audiences.
Chronology of Development: From Blog Post to Motion Graphics
The conceptual framework for Kosara’s 2021 video was established over a decade ago. In 2008, Kosara published a seminal blog post on EagerEyes titled "Linear vs. Quadratic Change," which outlined the dangers of scaling shapes by area versus length. While the post became a staple reference for data visualization students, its transition into a modern video format was catalyzed by contemporary professional discourse.
In early 2021, a conversation on the then-nascent social audio platform Clubhouse served as the primary motivator for the project. During a session involving Cole Nussbaumer Knaflic, the founder of Storytelling with Data and a leading voice in the industry, the topic of historical visualization pitfalls was revisited. Knaflic’s reminder of the 2008 post prompted Kosara to modernize the content for a visual-first audience.
The production of the video also coincided with the viral spread of several controversial infographics during the COVID-19 pandemic and the 2020 election cycle. One specific infographic, which Kosara utilized in his thumbnail and analysis, drew criticism for its use of exaggerated icons to represent demographic shifts. By June 15, 2021, the final video was released, marking a departure from Kosara’s previous "talking head" style. The new iteration utilized 100% motion graphics to demonstrate the mathematical concepts of scaling in real-time, allowing viewers to see the area expansion as it occurred.
Historical Context: The ISOTYPE Solution
To provide a solution to the problem of quadratic distortion, Kosara points toward the ISOTYPE (International System of Typographic Picture Education) method. Developed in the 1920s and 30s by social scientist Otto Neurath and illustrator Gerd Arntz, ISOTYPE was designed as a "visual language" to communicate complex social and economic statistics to a broad, often undereducated, public.
The core tenet of ISOTYPE is the "multi-unit" principle. Neurath famously argued that "greater quantities should be represented by a greater number of signs of the same size, not by a larger sign." If one icon of a person represents 10,000 people, then 50,000 people should be represented by a row of five identical icons, rather than one giant icon that is five times as tall. By using a repetitive grid of icons, the ISOTYPE method ensures that the total area occupied by the graphics remains perfectly proportional to the data. This eliminates the risk of quadratic or cubic distortion and provides a clear, countable metric for the viewer. Kosara’s video emphasizes that while ISOTYPE is nearly a century old, its principles remain the gold standard for honest pictorial data representation.
Supporting Data and the "Lie Factor"
The concept of visual distortion was famously quantified by Edward Tufte in his 1983 book, The Visual Display of Quantitative Information. Tufte introduced the "Lie Factor," a ratio used to measure the degree of distortion in a graphic:
$$Lie Factor = fracSize of effect shown in graphicSize of effect in data$$
If the Lie Factor is greater than 1.05 or less than 0.95, the graphic is considered significantly misleading. In the case of quadratic scaling, where a 2x increase in data results in a 4x increase in area, the Lie Factor would be 2.0 ($4 / 2$). If a designer scales a 3D object (like a sphere or a cube) to represent a 2x increase, the volume increases by 8x ($2^3$), resulting in a staggering Lie Factor of 4.0.
Kosara’s work highlights that these errors are rarely malicious; rather, they are the result of software defaults and a lack of mathematical training among graphic designers. Most modern design tools, such as Adobe Illustrator or Canva, scale objects proportionally by default. When a designer drags the corner of an icon to make it "twice as big," the software doubles both the X and Y axes, inadvertently creating the quadratic distortion that Kosara warns against.
Industry Reactions and Professional Implications
The release of Kosara’s video sparked renewed debate within the data visualization community regarding the ethics of "infographic-style" charts. While professional data scientists and analysts generally favor minimalist bar charts (as advocated by figures like Stephen Few), the marketing and journalism sectors often prefer pictorial charts for their engagement value and "shareability" on social media.
Cole Nussbaumer Knaflic and other experts have noted that while pictorial charts are effective at grabbing attention, the responsibility lies with the creator to ensure the "visual weight" matches the data. Reactions from the design community following Kosara’s video suggested a growing interest in "unit charts"—a modern adaptation of ISOTYPE—where individual dots or icons represent fixed values. This approach is increasingly seen in high-end data journalism, such as that produced by The New York Times or The Pudding, to explain complex social issues like wealth inequality or racial disparities.
Furthermore, Kosara’s experiment with a pure motion-graphics format reflects a broader shift in educational media. By removing the "talking head" and focusing entirely on the visual manipulation of data, the video caters to a more technical audience that values clarity and direct demonstration over personality-driven content. Kosara acknowledged that this approach is significantly more labor-intensive, requiring precise timing and animation to ensure the mathematical concepts align with the narration.
Broader Impact on Data Literacy
The implications of Kosara’s analysis extend far beyond the niche of graphic design; they touch upon the broader issue of data literacy in the digital age. As infographics become the primary vehicle for news consumption on platforms like Instagram and X (formerly Twitter), the potential for "visual misinformation" grows. A viewer may only glance at an image for three seconds; in that time, their brain registers the massive size of an icon before their mind can process the actual numbers written in small text.
By highlighting the "linear vs. quadratic" trap, Kosara provides a framework for viewers to become more critical consumers of information. The video serves as a reminder that visualization is not merely an art form but a branch of applied mathematics. When the principles of geometry are ignored, the result is a breakdown in communication that can skew public perception of critical issues, from climate change to economic policy.
In conclusion, Robert Kosara’s "Linear vs. Quadratic Change" is a vital contribution to the ongoing effort to standardize integrity in visual communication. By bridging the gap between 20th-century ISOTYPE principles and 21st-century motion graphics, the project reinforces the necessity of proportional representation. As the volume of data generated globally continues to expand, the tools used to represent that data must remain anchored in mathematical truth, ensuring that the "picture" we see is an accurate reflection of the reality it claims to describe.